Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11719244 | C2 | semidirect |
| 5. #11718670 | C2 | semidirect |
| 6. #11718539 | C2 | semidirect |
| 7. #11718535 | C2 | semidirect |
| 8. #11718424 | C2 | semidirect |
| 9. #11718422 | C2 | semidirect |
| 10. #11718344 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 45. C13×D8 | Q8 | semidirect |
| 153. D8 | Dic26 | semidirect |
| 175. C13 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719244 | 2 |
| C4×C13×D8 | 2 |
| D8×Dic13 | 2 |
| #11718670 | 2 |
| #11718539 | 2 |
| #11718535 | 2 |
| #11718424 | 2 |
| #11718422 | 2 |
| #11718344 | 2 |
| C8×Dic26 | 2 |
| #3380 | 13 |